Vertex-fault-tolerant cycles embedding in balanced hypercubes

The balanced hypercube is a new variant of the hypercube, which was proposed by Wu and Huang. Xu et al. (2007) proved that every edge of an n-dimensional balanced hypercube Nit, lies on a cycle of every even length from 4 to 2(2n) In this paper, we consider the v edge-bipancyclicity of BHn with faulty vertices. Let F v be the set of faulty vertices in BHn with F-v T, < n - 1. We show that every fault-free edge of BHn F lies on a fault-free cycle of every even length from 4 to 2(2)n(') 21F11, where n 1. Our result improves the previous best result by Xu et al. in terms of fault-tolerant vertices.